This thesis describes the construction of an undirected network (e.g. road network) model, based on the recently developed higher-order active contours (HOACs) and phase fields, and introduces a new family of phase field HOACs for directed networks (e.g. hydrographic networks in remote sensing imagery, vascular networks in medical imagery). In the first part of this thesis, we focus on the stability analysis of a HOAC energy leading to a ‘phase diagram'. The results, which are confirmed by numerical experiments, enable the selection of parameter values for the modelling of undirected networks.

Hydrographic networks, unlike road networks, are directed, i.e. they carry a unidirectional flow in each branch. This leads to specific geometric properties of the branches and particularly of the junctions, that it is useful to capture in a model, for network extraction purposes. We thus develop a nonlocal phase field model of directed networks, which, in addition to a scalar field representing a region by its smoothed characteristic function, and interacting nonlocally so as to favour network configurations, contains a vector field representing the ‘flow' through the network branches. The vector field is strongly encouraged to be zero outside, and of unit magnitude inside the network; and to have zero divergence. This prolongs network branches; controls width variation along a branch; and produces asymmetric junctions for which total incoming branch width approximately equals total outgoing branch width. In conjunction with a new interaction function for the scalar field, it also allows a broad range of stable branch widths. The new proposed model is applied to the problem of hydrographic network extraction from VHR satellite images, and it outperforms the undirected network model.

We address the problem of quasi-automatic extraction of directed networks, which have characteristic geometric features, from images. To include the necessary prior knowledge about these geometric features, we use a phase field higher-order active contour model of directed networks. The model has a large number of unphysical parameters (weights of energy terms), and can favour different geometric structures for different parameter values. To overcome this problem, we perform a stability analysis of a long, straight bar in order to find parameter ranges that favour networks. The resulting constraints necessary to produce
stable networks eliminate some parameters, replace others by physical parameters such as network branch width, and place lower and upper bounds on the values of the rest.We validate the theoretical analysis via numerical experiments, and then apply the model to the problem of hydrographic network extraction from multi-spectral VHR satellite images.

We propose a new algorithm for network segmentation from VHR remote sensing images. The algorithm performs this task quasi-automatically,
that is, with no human intervention except to fix some parameters. The task is made difficult by the amount of prior knowledge about network region geometry needed to perform the task, knowledge that is usually provided by a human being. To include such prior knowledge, we make use of methodological advances in region modelling: a phase field higher-order active contour of directed networks is used as the prior model for region geometry. By adjoining an approximately conserved flow to a phase field model encouraging network shapes (i.e. regions composed of branches meeting at junctions), the model favours network regions in which different branches may have very different widths, but in which width change along a branch is slow; in which branches do not
come to an end, hence tending to close gaps in the network; and in which junctions show approximate ‘conservation of width’. We also introduce image models for network and background, which are validated using maximum likelihood segmentation against other possibilities. We then test the full model on VHR optical and multispectral satellite images.

{Phase diagram of a long bar under a higher-order active contour energy: application to hydrographic network extraction from VHR satellite images},

year

=

{2008},

month

=

{décembre},

booktitle

=

{International Conference on Pattern Recognition (ICPR)},

address

=

{Tampa, Florida},

url

=

{https://hal.inria.fr/inria-00316619},

pdf

=

{http://hal.inria.fr/docs/00/31/66/19/PDF/icpr08aymenelghoul.pdf},

keyword

=

{Phase diagram, Higher-order actif contours, Forme, river extraction}

}

Abstract :

The segmentation of networks is important in several imaging domains, and models incorporating prior shape knowledge are often essential for the automatic performance of this task. Higher-order active contours
provide a way to include such knowledge, but their behaviour can vary significantly with parameter values: e.g. the same energy can model networks or a ‘gas of circles’. In this paper, we present a stability analysis
of a HOAC energy leading to the phase diagram of a long bar. The results, which are confirmed by numerical experiments, enable the selection of parameter values for the modelling of network shapes using the energy.
We apply the resulting model to the problem of hydrographic network extraction from VHR satellite images.